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House Price Efficiency: Expectations, Sales, Symmetry
Arthur Grimes, Andrew Aitken, Suzi Kerr
Motu Working Paper 04–02 Motu Economic and Public Policy Research
May 2004
Author contact details Arthur Grimes Corresponding Author Motu Economic and Public Policy Research PO Box 24390 Wellington New Zealand Email: [email protected] Andrew Aitken Motu Economic and Public Policy Research Email: [email protected] Suzi Kerr Motu Economic and Public Policy Research Email: [email protected]
Acknowledgements We wish to acknowledge, with thanks, the assistance of three funders for making this research possible: Lincoln Institute of Land Policy, Centre for Housing Research Aotearoa New Zealand, and the New Zealand Foundation for Research Science and Technology (Programme on Understanding Adjustment and Inequality).
Motu Economic and Public Policy Research PO Box 24390 Wellington New Zealand Email [email protected] Telephone +64-4-939-4250 Website www.motu.org.nz
© 2004 Motu Economic and Public Policy Research Trust. All rights reserved. No portion of this paper may be reproduced without permission of the authors. Motu Working Papers are research materials circulated by their authors for purposes of information and discussion. They have not necessarily undergone formal peer review or editorial treatment. ISSN 1176-2667.
Abstract An efficient housing market is of critical importance for individual
welfare and for a well-functioning economy. We test the efficiency of this market
by estimating the factors that determine both the long-run and the dynamic paths
of regional house prices. Our tests use a new quarterly regional panel data set
covering the 14 regions of New Zealand from 1981 to 2002. The tests indicate that
regional housing markets converge to an equilibrium consistent with consumer
optimising conditions, and hence with long-run efficiency. However, some
conditions required for short-run (dynamic) efficiency are violated. We find that
extrapolative price expectations, based on past regional phenomena, lead to
overshooting of house prices in response to new region-specific information. We
also find that price dynamics are influenced by past regional house sales activity
and that the dynamic adjustment process is asymmetric depending on whether
house prices are above or below their long-run equilibrium.
JEL classification G14, R21, R31 Keywords House prices; housing appreciation; housing market; adjustment dynamics
Contents 1 Introduction..................................................................................................... 1
2 Theoretical model ........................................................................................... 4 2.1 Long-run model ...................................................................................... 5 2.2 Issues in implementing the long-run model ........................................... 6 2.3 Dynamic model .................................................................................... 10
3 Data .............................................................................................................. 14
4 Results........................................................................................................... 16 4.1 Long-run results.................................................................................... 16 4.2 Dynamic results: Symmetric ................................................................ 19 4.3 Dynamic results: Asymmetric .............................................................. 22 4.4 Dynamic results: Non-linear................................................................. 25
5 Interpretation................................................................................................. 26
6 Conclusions................................................................................................... 30
References ............................................................................................................. 37
Tables Table 1: Sales price summary statistics, population and activity ......................... 32
Table 2: Results of panel unit root tests ............................................................... 32
Table 3: Long-run house price estimates.............................................................. 33
Table 4: Dynamic house price estimates .............................................................. 34
Table 5: Sales (Szt) response to house price developments .................................. 35
1 Introduction An efficient housing market is of critical importance for individual
welfare and for a well-functioning economy (Di, 2001; Bajari and Kahn, 2003).
Long-run efficiency requires that house prices converge to a relationship
determined by consumers' optimising conditions. Short-run efficiency requires
prices to adjust quickly to new information so that excess profit opportunities,
after deducting trading costs, do not linger in the market.
We test for long-run and short-run efficiency of the housing market, as
reflected in house prices. Our tests indicate that regional housing markets
converge to an equilibrium consistent with long-run efficiency. However, some
conditions required for short-run efficiency are violated. In particular, we find that
extrapolative price expectations, based on past regional phenomena, lead to
overshooting of house prices in response to new region-specific information.
Further, price dynamics are influenced by past regional house sales activity.
Notably, the dynamic adjustment process is asymmetric depending on whether
house prices are above or below their long-run equilibrium. Thus the degree of
short-run efficiency is affected by the nature of a shock's impact (upwards or
downwards) on the equilibrium price.
Our tests use a new regional panel data set covering the 14 regions of
New Zealand over 88 quarters [1981(1)–2002(4)]. This dataset includes the
median sales price of owner-occupied dwellings, the ratio of the dwelling's sales
price to its official valuation (used for property tax purposes), and the number of
sales in each quarter. We use this data in conjunction with other relevant regional
data to test the efficiency properties of the housing market. The sales data enables
us to test for sales-driven "fad" (or other) effects that existing studies either cannot
test or have to test using inadequate proxies. Our finding that sales activity has a
material, but asymmetric, effect on house price dynamics adds to current
understanding of the nature of property market dynamics.
1
We illustrate our key findings relating to inefficiency of house price
dynamics through simulated house price paths in response to certain economic
and financial shocks. Plausible economic developments, based on recent historical
experience, indicate the potential for material house price overshooting.
House prices summarise a large amount of information regarding the
desirability and cost of living in a particular location (MacDonald and Taylor,
1993; Case and Mayer, 1996; Sheppard, 1999; Cook, 2003) and influence
migration patterns (Glaeser and Gyourko, 2001). Recent studies have cast doubt
on the efficiency of this market. For instance, Capozza and Seguin (1996) find
evidence of euphoria in metro house markets, while Case and Shiller (1988, 1989,
2003) find evidence of predictability in regional house prices that should not exist
in an efficient market. Inefficiency in such a critical market may have important
welfare consequences and may cause financial imbalances, especially following
the bursting of a bubble, with material macroeconomic consequences.1
Case and Shiller (2003) define a housing bubble as "a situation in which
excessive public expectations for future price increases cause prices to be
temporarily elevated". They postulate that fundamental factors such as income
growth and interest rates initiate a house price change, but expectations may then
become self-reinforcing, setting a bubble in train. Their survey-based results
indicate that house buyers in markets with recent high house price growth build in
high expected capital gains for the following decade. This behaviour is consistent
with an expectations-driven bubble. They also produce survey evidence that house
market adjustment is likely to be asymmetric, with sellers preferring to withdraw
from the market during a downturn rather than accepting the price consequences
of selling in those market conditions. By contrast, in an upturn, house prices
respond rapidly, albeit being curtailed longer term by new house construction.
1 Concerns over such issues led The Economist magazine to devote its 31 May 2003 survey of property to this topic under the title "Close to bursting".
2
This paper builds on these insights, presenting a systematic examination
of the sources of potential inefficiencies in regional housing markets. We estimate
the factors which determine both the long-run and dynamic paths of regional
house prices. We do so by adopting an optimising model of house price
determination, which we use to estimate long-run house price determinants.
Expectations are a key factor in this formulation. We then estimate clearly
specified dynamic models, and test whether certain features discussed by Case
and Shiller (1989, 2003) and others influence the dynamic behaviour of the
housing market. These features may push prices temporarily away from
equilibrium. Our analysis is at a regional level and incorporates both regional and
national variables, as appropriate, within a panel cointegration framework. This
approach complements the survey-based and single equation approaches of Case
and Shiller (1989, 2003). By testing hypotheses within a rigorous theoretical and
econometric framework, and with an alternative dataset incorporating sales
variables not available to previous researchers, we are able to shed considerable
light on the (efficient and inefficient) behaviour of the housing market.
The questions we address in order to assess long run and short run
efficiency, include: Are prices in the long term driven by factors identified
through a consumer optimization problem? Do expectations-driven fads have an
impact and, if so, are these fads driven by regional or national developments?
Does regional sales activity have an effect in fuelling regional fads, or is sales
activity a stabilising factor driving prices towards equilibrium? Do the dynamic
adjustment mechanisms incorporate non-linearities which may indicate
information-based reasons for variations in price adjustment towards long run
equilibrium? Do significant adjustment asymmetries exist and, if so, what do
these asymmetries indicate about the nature of fads or related phenomena?
3
We address this set of questions using a new, consistently measured
quarterly panel dataset for New Zealand. The country has a population of 4
million people spread over two main islands. With a combined land area similar to
that of Japan or the United Kingdom, it is divided into 14 regions corresponding
to Regional Councils.2 Regional Council boundaries follow physical features—
primarily major water catchments—so regions tend to be distinct economic
entities; for instance, individual cities do not flow over council boundaries.3
The paper is arranged as follows. Section 2 outlines the theoretical basis
for our long-run model and explicitly formulates the long-run and dynamic
models to be tested. Data is described in Section 3, and estimation results are
presented in Section 4. Interpretation of the dynamic results, focusing especially
on the effects of capital gains expectations, sales activity and asymmetric
adjustment processes on house price dynamics, is presented in Section 5. Section
6 presents a brief conclusion, with pointers to future work.
2 Theoretical model Our theoretical approach to estimating regional house prices builds on
the work of Pain and Westaway (1996), who formulated an optimising model to
determine equilibrium house prices. We use this model as a basis for examining
long-run efficiency of the housing market. We then incorporate error correction
and dynamic adjustment aspects introduced by Capozza et al (2002) plus
additional dynamic adjustment features to investigate aspects of short-run
efficiency discussed above.
2 There are 16 Regional Councils but, in keeping with our data sources, we amalgamate 3 small neighbouring councils into one (Nelson-Marlborough-Tasman). 3 The physical distinctiveness of regions is reflected in the finding that New Zealand house prices do not share a single common trend, so national variables alone cannot explain regional house price developments (Grimes et al, 2003).
4
2.1 Long-run model Pain and Westaway formulate the consumer problem as one where each
household allocates its lifetime wealth over consumption of housing services (ch;
proxied by a constant, θ, multiplied by the housing stock, h) and non-housing
consumption (c) in each period of life and over its bequest. Use of a constant
relative risk aversion utility function (with coefficient of relative risk aversion, γ)
and aggregating over individuals results in the optimising equation explaining
equilibrium real house prices (g) in (1):
ln(g) = (1 – γ)ln(θ) – γln(h) + γln(c) – ln(UC) (1)
where:
• g is the ratio of quality-adjusted price of housing (ph) to the price of
non-housing consumption goods (pc)
• h is the housing stock
• c is non-housing consumption
• UC is the real user cost of capital (discussed further below).
If c is unobservable (as it is with the regional data at our disposal), we
can add an auxiliary hypothesis that c is determined as in (2):
ln(c) = α + βln(y) (2)
where: y is an appropriate activity variable influencing regional non-
housing consumption.4
4 Note that c represents aggregate non-housing consumption, so y represents aggregate economic activity; no additional demographic scalar is required. If we were to make c also a function of UC in (2), it would not alter the nature of our final estimating equations, although interpretation of the UC coefficient would differ. (2) and subsequent equations also include error terms; these are assumed to have standard properties, but are suppressed for expositional purposes.
5
House prices are observed for bundles of housing and related
services.5,6 If (as in our case) house sales price data are not quality adjusted, we
can add another auxiliary hypothesis linking the real unadjusted sales price (pu/pc)
to the quality adjusted sales price as in (3):
ln(pu/pc) = ln(ph/pc) + ξZ (3)
where: Z is a vector of house-specific and locality-specific attributes
and ξ is an accompanying coefficient vector. Combining (1)–(3) yields:
ln(pu/pc) = δ – γln(h) + βγln(y) – ln(UC) + ξZ (4)
where: δ = [(1 – γ)ln(θ) + αγ].
2.2 Issues in implementing the long-run model The stock of housing (h) in each area is determined jointly with house
prices in the long run. The rate of change in the stock of houses will be influenced
by factors such as costs of constructing new houses, the degree of vacant land
available for housing and regulatory efficiency (Capozza et al, 2002; Case and
Mayer, 1996; Glaeser and Gyourko, 2002). The housing stock changes only
slowly over time and so can be considered a predetermined variable over short to
medium time horizons. By contrast, the house price is an asset price and so is a
"jump" variable, reflecting the influence of new information. We can therefore
estimate (4) and identify the effect of changes in each of h, y and UC on long-run
real house prices.7
5 House-specific services have been proxied elsewhere through: number of bathrooms, lot size, fireplace, garage size, air-conditioning, basement, detached dwelling, patio and previous dwelling purchase price (Can, 1992; Dubin, 1992; Genesove and Mayer, 2001). 6 Housing services also include amenity and location values, which have been proxied elsewhere through: neighbourhood quality index, land supply index, coastal situation, distance from city centre, school assessment scores, crime rate, per capita income and unemployment rate (Can, 1992; Capozza et al, 2002; Case and Mayer, 1996; Dubin, 1992; O'Donovan and Rae, 1997). 7 Eventually h will adjust, so the long-run system-wide effect of a change in each explanatory variable on house prices has to incorporate the housing stock response. O'Donovan and Rae (1997) found that single equation estimates of aggregate New Zealand house prices gave very similar results to full system estimates, which included equations also for consumption and for housing investment.
6
The variables which enter Z may include some that are fixed over time
but which vary cross-sectionally (e.g. latitude of the locality) and others which
vary over time (e.g. changing house quality or changing amenities within a
locality). The former set can be handled through the inclusion of fixed effects. The
latter require region-specific proxies. These quality and amenity variables are
likely to be slowly changing over time (e.g. the process of "gentrification" of an
area, or changing attitudes towards a coastal location). If (as in our case) there is
no comprehensive data to proxy for the latter elements of Z, we can capture the
influence of these variables through inclusion of a quadratic time trend, with
coefficients that are freely estimated for each region reflecting trends in region-
specific attributes. Thus, if the quality of residential houses in one region is
trending upwards relative to another region, the quadratic time trend can account
for this and other (quadratically) trending factors.8
A key variable in (4) is UC, the real user cost of capital. In formulating
this variable we note that, in New Zealand, owner-occupiers' mortgage interest
payments are not tax deductible, nor are capital gains from housing taxed. If loan
finance is the marginal source of finance for housing then there is no tax relief on
the housing loan and no tax to pay on the housing services. Thus no tax rate
should appear in the UC variable.9
The relevant real user cost facing a house purchaser is the real interest
rate, r,10 less the expected annual real capital gain on the house, ġ. The real
interest rate is identical across regions in any given quarter, but ġ may not be. As
discussed by Case and Shiller (2003), the nature of capital gains expectation
formation is of importance to any fad or overshooting effect.
8 By restricting our attention solely to residential houses, we avoid change in housing quality caused by a shift from detached dwellings to apartments. In our dynamic equations, changes in composition of houses sold each quarter are also accounted for. 9 If, however, other taxable investment opportunities constitute the marginal source of finance for funding house purchase then the tax rate should enter into UC, since the opportunity cost is taxed. Also, housing investors' interest payments are tax deductible. This leads to the problem that different investors face different tax rates and the relationship of these tax rates to each other has varied over time. Entering a single tax rate would not adequately capture the taxation effect for different individuals. 10 We proxy r by the 90-day bank bill yield less the latest CPI inflation rate, each expressed in annual terms. Grimes (1994) finds that mortgage interest rates are set as a margin above the 90-day bank bill yield; the margin is incorporated into the equation constant.
7
The more backward looking expectations are, the more likely it is that
prices can overshoot their fundamental values in response to a change in
fundamental factors. We test four alternative proxies for ġ.
First, building on O'Donovan and Rae's (1997) nationwide analysis of
the New Zealand housing market, we set ġ equal to the past three years' annual
real capital gain on houses at the national level.11 The three-year horizon reflects
expectations based on the medium-term national trend in real prices. We call the
resulting user cost variable UC1. Given its construction, it is identical across
regions in any given quarter.
Second, we set ġ equal to the past three years' annual real capital gain
on houses at the regional level. The resulting user cost variable, UC2, differs
across regions in any given quarter.
Third, we set ġ equal to the past year's annual real capital gain on
houses at the regional level. The one-year horizon reflects expectations driven by
shorter term factors, consistent with Case and Shiller's (1989) finding that one
year's house price changes help predict the next year's price change. The resulting
user cost variable, UC3, also differs across regions in any given quarter.
Fourth, we set ġ equal to zero, allowing the equation constant to proxy
for a constant real capital gain expectation over time. We denote this variable as
UC4. If there is no backward-looking element in expectations, this proxy should
perform better than each of the other three proxies.
As in O'Donovan and Rae (1997), we note that each of the four
alternative proxies approaches zero, and at times becomes negative during our
sample. This makes it impossible to include ln(UC) as specified in (4). Instead, we
include UC with a freely estimated coefficient.
11 We take the average of the first and fourth years in constructing this variable to reduce noise. For instance, the 1985(1) observation is calculated as the annual rate of change between calendar 1981 and calendar 1984 average real house prices.
8
Another complication with UC in the New Zealand context is that
interest rates were strictly controlled until 1984 by government regulation and are
unlikely at that stage to have equilibrated the credit market. (The shadow cost of
credit is likely to have been considerably above the actual interest rate, reflecting
excess demand at the regulated rate.) To account for this factor, we enter UC
starting from 1985(1), and supplement it with the inclusion of a dummy variable
(UCD) taking the value of 1 prior to 1985(1) and 0 thereafter.
Taking each of the above factors into account, the long-run estimating
equation for each region corresponding to our theoretical specification (using
subsequent data terminology, with time subscript t) is:
Pzt = a0z + a1zYzt + a2z Hzt + a3zUCxzt + a4zUCDt + a5zTIMEt + a6zTIME2t (5)
where:
• Pz is the log of the real median residential house sales price in region
z [corresponding to ln(pu/pc)]
• Yz is the log of real regional economic activity for region z
[corresponding to ln(y)]
• Hz is the log of the residential house stock in region z [corresponding
to ln(h)]
• UCxz is the real user cost of capital (x = 1, 2, 3, 4 as described
above)
• UCD is a dummy variable = 1 prior to 1985(1), 0 thereafter
• TIME is a linear time trend
• TIME2 is the linear time trend squared.
a0z–a6z are coefficients with a1z, a2z, a3z and a4z each constrained to be
identical across regions, reflecting the coefficients in (4); a0z, a5z and a6z are
coefficients that reflect fixed and region-specific trend effects and so differ across
regions.
9
For our estimates to be consistent with long-run market efficiency, (5)
has to be a valid long-run equation across all regions. As discussed below, the
stochastic variables included in (5) are non-stationary [I(1)]. A requirement for (5)
to be a valid long-run equation, and hence for the equation to be consistent with
long-run efficiency holding, is that the residual from (5) is stationary; if this were
not the case, real house prices would not return to the consumer's optimising
conditions following a shock. In particular, we require the residual to be stationary
when a1z, a2z, a3z and a4z are each restricted to be identical across regions, since in
each case the relevant coefficient reflects underlying parameter(s) that are
hypothesised to be identical across regions.
2.3 Dynamic model Market efficiency is most often tested through examination of price
dynamics (Fama and French, 1988; Case and Shiller, 1989; Capozza & Seguin,
1996). As Capozza and Seguin demonstrate, however, short-run market efficiency
cannot be tested solely through an examination of house price dynamics, since
rentals also form part of the return to housing. Without information on rentals, we
cannot interpret directly whether the dynamics of house prices are consistent with
a no arbitrage condition.
Instead, we focus on the speed and nature of the adjustment of house
prices to long-run equilibrium, defined in (5), noting—to anticipate the empirical
results—that (5) passes the tests to be considered a valid long-run specification of
house prices. In a perfectly flexible market with zero transactions costs and no
information costs, house prices should adjust immediately to their long-run values
consequent on a change in one or more of the explanatory variables in (5). Even if
this were the case, stochastic errors could cause temporary deviations in the house
price from long-run equilibrium, but in an efficient market these deviations should
be fully unwound in the subsequent quarter.
10
These conditions can be specified within an error correction framework.
Denote the equilibrium value of the log of the real unadjusted long-run house
price [from (5)] as P*zt, and consider the error correction equation (6):
∆Pzt = b1z∆P*zt + b2z(Pzt–1 – P*zt–1) + b3z∆Pzt–1 + b4zXzt (6)
Inclusion of ∆Pzt–1, the lagged change in real house prices, allows for a
partial adjustment mechanism.12 Xzt is a vector of other stationary variables that
may potentially impact on the dynamics of real house prices in region z. Short-run
market efficiency, as discussed above, requires b1z = 1 for all z, b2z = –1 for all z,
b3z = 0 for all z, and b4z = 0 for all elements of X and all z.13
The specification in (6) is appropriate for an environment of costless
information dissemination about fundamentals. Capozza et al (2002) examine the
case where increased housing market activity improves information dissemination
about the market price (and quality) of houses. In this imperfect information world
the adjustment coefficients, b1z and b2z in (6), may themselves be a function of
housing market activity. Our house sales data corresponds to a direct measure of
housing market activity, unlike Capozza et al who did not have a direct proxy for
such activity. Building on their approach, we model this imperfect information
environment by allowing the serial correlation and reversion parameters in the
dynamic equation for each region to be functions of a housing market activity
variable specific to a region as in (7):
∆Pzt = b1z∆P*zt + [b2z+b2Az(Azt – Ā)]( Pzt–1 – P*zt–1) + [b3z + b3Az(Azt – Ā)]∆Pzt–1 + b4zXzt (7)
12 The relative values of b1z, b2z and b3z in each region determine the degree of lagged adjustment and/or overshooting behaviour relative to fundamentals. Capozza et al (2002) demonstrate that as the serial correlation coefficient, b3z, increases, the amplitude and persistence of house price cycles tends to increase. As the absolute value of the reversion coefficient, b2z, increases, the frequency and amplitude of the cycle tends to increase. 13 A single exception to the latter requirement in our estimated equation is a freely estimated coefficient on a variable (COMP) which accounts for short-term measured price changes due to changing composition of house sales between quarters within each region. For instance, if a higher ratio of "good" houses sells in one quarter than in the previous quarter, we would expect to see measured sale prices rise (temporarily) from one quarter to the next.
11
In (7), Az is an independent variable influencing adjustment of house
prices in each region and Ā represents the mean value of Az. In this specification,
for instance, a region that has a value of Azt greater than Ā will have faster
reversion of prices to fundamentals than the mean speed of reversion if b2Az is
negative.
In operationalising (7), there is an issue as to whether the mean value
(Ā) should be time invariant as postulated by Capozza et al. For variables that are
trending over time, this specification would imply a gradual raising or lowering of
the partial adjustment and reversion parameters. In some cases this may be
economically sensible but in others it will not be. We consider that the most
robust way of specifying the Az variable is to choose a form of the variable which
does not trend significantly over the sample period, so that the sample mean is a
stable baseline against which to measure deviation of actual movements from the
norm. Our measure of Az is the ratio of house sales to the housing stock in each
region.14 If sales rise, we hypothesise that there will be improved information
dissemination; hence we expect b2Az ≤ 0, which corresponds to faster reversion to
long-run equilibrium (where –1 < b2z < 0). If sales activity coupled with lagged
price changes incorporates new and/or improved information, we would expect
b3Az ≥ 0. Interpretation of these coefficients will indicate whether market
efficiency is affected by information disseminated through house sales activity.
Sales activity should have no effect additional to that specified in (7) in
an efficient market (i.e. if it is entered as a component of Xzt, its coefficient should
be zero). However, it may be, as suggested by Case and Shiller (1989), that sales
activity does affect price dynamics independently of the information reasons just
outlined. To test if this is the case, we add current and lagged sales activity
independently to the equation (affecting the constant term) as in (8). In (8) the
current and lagged activity variables test whether sales activity has an independent
effect on price adjustment over and above the interaction terms in (7).
14 Capozza et al used population as an imperfect proxy for sales. However, house sales are more likely to capture dynamic effects than is a slow-moving variable such as population. We also have data (albeit for only half the full period) for building consents, reflecting forthcoming house construction activity. However, the partial coverage of this variable meant it was not statistically significant when included in our work and we do not discuss its role further here.
12
∆Pzt = b1z∆P*zt + [b2z + b2Az(Azt – Ā)]( Pzt–1 – P*zt–1) + [b3z + b3Az(Azt – Ā)]∆Pzt–1
+ b4zXzt + Σib5izAzt–i (8)
The vector, Xzt, now excludes sales activity. It remains the case that
short-run efficiency requires b4z = 0 and b5iz = 0 for all i.
Our final test of the dynamic structure of house prices is a test for
asymmetric adjustment depending on whether the previous quarter's actual prices
are above or below fundamentals. Glaeser and Gyourko (2001), Cook (2003) and
Case and Shiller (2003) all indicate the potential importance of asymmetric
adjustment for the dynamics of the housing market. If regional housing demand
expands, say in response to an increase in regional economic activity, prices are
expected to rise from (5) but housing supply (h) will also expand gradually over
time. By contrast, if regional housing demand falls, housing supply is unlikely to
contract materially other than through depreciation (Glaeser and Gyourko, 2001).
The effects of these asymmetric factors on expectations may be reflected in
asymmetric adjustment to equilibrium in the two situations, with prices reacting
more strongly to a fall in equilibrium prices than to a rise. Another cause of
asymmetry (working in the opposite direction) may be reluctance by previous
buyers to experience a realised capital loss in situations where prices have fallen.
Sales may reduce in such circumstances without a significant observed price fall
(Genesove and Mayer, 2001).
We test whether coefficients in (8) are identical when the sample is split
into two categories: Pzt–1 > P*zt–1 and Pzt–1 < P*zt–1. If identical, then adjustment is
symmetric; otherwise asymmetric adjustment is indicated. Asymmetric
adjustment may indicate inefficiencies under some market conditions, as in the
“reluctant-seller” (Genesove and Mayer) case cited above. Interpretation of the
coefficients in the split sample will yield insights into what is driving any
asymmetry.
13
3 Data We use Quotable Value New Zealand (QVNZ) data for median
residential house sale prices in each region. QVNZ is a state-owned entity that
collects data on all house sales and which also values properties for local authority
property tax purposes. We have measures, from this source, of the number of
house sales in each region, the QVNZ valuation of houses that are sold, and the
median sales price. Each of these variables is used in the estimation in Section 4.
In order to compare "like with like" as much as possible, we restrict our attention
to the residential house market, which excludes all multi-unit residential sales and
all non-residential transactions. All data is available quarterly from 1981(1) –
2002(4). These data, together with data for the regional housing stock, are
described in detail in Grimes et al (2003). That paper also presents tests for
bivariate cointegration between regional house price levels and bivariate
contemporaneous correlation between regional house price changes. These tests
indicate that while house prices are cointegrated for some regional pairs they are
more frequently not cointegrated. A little over half the contemporaneous
correlations are significant at the 5% level. Together, these results indicate some
similarity in house price developments nationally, but also reveal material
elements of regional diversity.15
Regions are denoted RC01-RC15 (there is no region 10); RC01-RC0916
are in the North Island, RC11-RC1517 are in the South Island. Table 1 lists key
characteristics of the data for each region. Column 1 presents the median nominal
sales price for the 2002 calendar year, demonstrating that the median price in
Auckland (RC02), New Zealand's largest city, was 4.5 times that in the (rural)
West Coast of the South Island (RC12). Column 2 presents the change in real
sales price between 1981 and 2002 (i.e. after deflating the median sales price by
the consumers price index, CPI).
15 Grimes et al also conduct Granger causality tests on regional house prices for all regional pairings, in both directions. Three-quarters of the 182 tests are not significant at the 10% level, implying that spatial autocorrelation is not material at the regional council level. 16 Northland, Auckland, Waikato, Bay of Plenty, Gisborne, Hawke's Bay, Taranaki, Manawatu-Wanganui and Wellington respectively. 17 Nelson-Marlborough-Tasman, West Coast, Canterbury, Otago and Southland respectively.
14
Real prices in Southland (RC15) fell by 27% over this period, while
those in Gisborne (RC05) were virtually unchanged; both regions are
predominantly rural with no city having a population in excess of 47,000. By
contrast, real prices in Auckland more than doubled and those in Wellington
(RC09), the capital city, almost doubled. The average number of quarterly sales
throughout the sample for each region is shown in column 3; column 4 lists the
population of each region at the 2001 census; column 5 presents population
density at the 2001 census.
In order to proxy real regional economic activity (Yzt), we use the
logarithm of the National Bank of New Zealand Regional Economic Activity
indices (National Bank of New Zealand, 2003). Column 6 of Table 1 indicates the
percentage change between 1981 and 2002 in this variable for each region. As
with previous columns, considerable divergence in regional performance is
indicated. Growth in the fastest growing region (Northland, RC01) was over three
times that in Gisborne (RC05). A comparison of columns 2 and 6 indicates that
fast-growing regions tended to have faster-growing real house prices; the (cross-
sectional) correlation between the two columns is 0.72.
In the dynamic equations we need to account for changes in the
composition of houses sold within a region in a particular quarter. To do so, we
use the QVNZ valuation (as opposed to sales price) data for the houses sold in
each quarter in each region. We form a composition variable, COMPz, which
takes the ratio of the median valuation of houses sold in a region relative to a
Hodrick-Prescott filtered series for that region's median house valuation, the latter
series representing the trend valuation of houses in the region. If the ratio in a
quarter is greater (less) than one, the median house sold in that quarter is better
(lower) quality than the average house in that region. Hence this variable should
enter the dynamic equation with a positive sign.18 The sales variable, Sz, which we
enter into the dynamic equation (representing the housing market activity variable,
Az) is the ratio of house sales to the housing stock in each region. House sales data
are obtained from QVNZ.
18 This variable is stationary and so does not appear in the long-run equation.
15
Each of Pz, Yz, Hz and UCxz are tested for non-stationarity using the
panel unit root tests of Levin, Lin and Chu (2002) and Im, Pesaran and Shin
(2002). We also test COMPz and Sz, which are each included in the dynamic
specification. Results are presented in Table 2. Where the results of these tests are
unambiguous (i.e. consistent from the 1% through to the 10% significance level)
the implied order of integration is indicated in Table 2; ambiguous results are
shown as I(0)/I(1).
Each of the variables, other than COMPz, is either unambiguously non-
stationary or else the order of integration cannot be determined with (near)
certainty. Where a result is ambiguous, we prefer to treat the series as non-
stationary, unless theory suggests that stationarity is more appropriate.19 Each of
the stochastic variables in (5) is therefore treated as being I(1).20 COMPz is clearly
I(0); Sz is also treated as I(0) since the sales to house stock ratio must be bounded
above and below, indicating stationarity.
4 Results
4.1 Long-run results We estimate (5) using both OLS and SUR, presenting results for each
estimation method.21 Initially we estimate the equation with no restrictions. To
provide a basis for comparison with our subsequent estimates, the Adjusted R2
and standard error (s.e.) for the system, using UC2, are 0.9988 and 0.0445
respectively.22 The s.e. indicates an average error of 4.5% across the sample,
which can be compared with an s.e. of 7.9% when the system is estimated with
just the fixed effects and quadratic time trend terms included.
We test the system of unrestricted equations for cointegration using the
group mean panel test of Pedroni (1999).23 The test statistic is –11.88 against a
19 See Banerjee et al (1993). 20 ADF tests on UC1 and UC4, both national variables, indicate that they are I(1) with drift. 21 Estimation is done in Stata and in Eviews. The Stata OLS results correspond to the Eviews WLS results. The SUR results are identical in each. 22 As shown in Table 3, UC2 provides the greatest explanatory power of all the UC variables. 23 This parametric ADF-based test is analogous to the Im et al unit root statistic applied to the estimated residuals of a cointegrating regression. The test allows for heterogeneity in both the
16
critical value of –1.46 indicating that the system of equations is cointegrated. Thus
the unrestricted estimates are consistent with a valid long-run specification.
When we restrict each of the coefficients a1z, a2z, a3z and a4z to be
identical across all regions, the Adjusted R2 and s.e. for the system are 0.9980 and
0.0485 respectively, little changed from the unrestricted estimates. Application of
the Pedroni panel cointegration test yields a test statistic of –8.33 against a critical
value of –6.28, which indicates that the restricted system is also cointegrated and
so represents a valid long-run specification for regional house prices. In terms of
efficiency, this finding implies that the housing market is consistent with long-run
efficiency, whereby house prices converge to values consistent with consumer
optimisation.
Table 3 presents the restricted OLS and SUR system estimates using
each of UC1–UC4. The results are used to examine the nature of the expectations
process for house prices. In each case a constant TIME and TIME2 are included
unrestricted for each region in addition to the four variables listed, but are not
reported in the table for clarity. The Adjusted R2 and s.e. for the system are
included for each estimation for comparison purposes.
The results are similar across the two estimation techniques, and show
consistency in sign and broad magnitude of coefficients across the different UC
specifications. However, the explanatory power of the equations differs
substantially across the different specifications of UC. By far the strongest
explanatory power comes with UC2, embodying region-specific real capital gains
expectations based on medium-term (past three-year) developments.
long-run cointegrating vectors as well as heterogeneity in the dynamics associated with short-run deviations from these cointegrating vectors.
17
The s.e. for each of the national specifications and for the one-year
region-specific specification of UC are all similar, and each is over 10% higher
than for the corresponding UC2 estimates. The coefficient estimates on UC are
considerably higher in absolute value for UC2 than for the other UC specifications
and the significance of those estimates is very much higher than for the other three
UC specifications. In the dynamic equations that follow, the greatest explanatory
power is also obtained using UC2 ahead of any of the other UC specifications. We
therefore restrict our attention to this definition of UC in the remainder of the
paper. The implications of the three-year region-specific UC specification for
house price dynamics are analysed in Section 5.
Restricting attention to the UC2 specification, the elasticity of real
house prices with respect to regional economic activity is approximately unity
(0.92 using SUR; 1.17 using OLS). As the housing stock expands, ceteris paribus,
the real price of housing falls with an elasticity of approximately two-thirds. Each
of these estimates appears intuitively reasonable.24 In most regions, the coefficient
on TIME is positive while the coefficient on TIME2 is negative. At the end of the
sample, the combined coefficient effect of TIME and TIME2 on Pz was positive in
ten of the fourteen regions.
A one percentage point increase in the real user cost of capital is
estimated to reduce the long-run real house price by between three-quarters of one
per cent and one per cent. Given that the real user cost of capital does not change
markedly over long periods, the long-run upward trend in real house prices in
most regions cannot be attributed to financial factors; rather, the upward trend in
real house prices is attributable mainly to increases in economic activity and to the
effects of tastes and other factors proxied by TIME and TIME2.
24 Compared with the underlying structural parameters in (4), the SUR estimates indicate a CRRA (γ) of 0.65 and a consumption elasticity with respect to economic activity (β) of 1.43. As discussed in Grimes et al (2003), our measure of the housing stock may involve some inaccuracy which could lead to the absolute value of the estimate for γ being understated, and hence to the implied estimate for β being overstated. (Any trend error in the housing stock estimate will be compensated for by inclusion of the quadratic time trend for each region.)
18
The positive coefficient on UCD indicates that real house prices were
higher, ceteris paribus, before financial deregulation than afterwards. The
regulated period was one in which real interest rates were frequently negative
(boosting house prices) while the supply of credit was restricted (reducing house
prices). The positive coefficient on UCD indicates that the former effect
outweighed the latter over the 1981–1984 period.
4.2 Dynamic results: Symmetric To test short-run efficiency, we start with the symmetric dynamic
framework in (8) with the interaction terms (b2Az and b3Az) constrained to zero.
The impact of the interaction terms is tested subsequently.
Recall that short-run efficiency requires that b1z = 1, b2z = –1, and
requires all other coefficients, other than the coefficient on COMPzt (accounting
for the effect of compositional changes in house sales on the measured median
price), to equal zero. We split ∆P*zt into its individual components (∆Yzt, ∆Hzt,
∆UC2zt) to test the short-run adjustment speed for each of its constituent parts. In
this case, the requirement that b1z = 1 corresponds to a requirement that the
coefficients on each of these components equal their long-run counterparts from
Table 3.
In the Xzt vector, we include COMPzt, as described above. We also
include the log change in consumer prices, ∆PCt. Inclusion of this variable allows
us to test whether aggregate consumer price changes are fully and immediately
incorporated into regional house price changes. If this is the case, the coefficient
on ∆PCt will be zero (i.e. b4z = 0). A coefficient between –1 and 0 indicates some
measure of partial adjustment of house prices to consumer price changes, in which
case changes to consumer price inflation will impact temporarily on real house
prices.
19
From (8), we include current and lagged sales activity, Szt–i, as our
measure of housing market activity. This variable tests for "bandwagon" or other
effects of sales activity on prices that arise separately from the information
dissemination role of sales posited by Capozza et al. In an efficient market, the
coefficients on these (current and lagged) sales variables should equal zero.
In estimating the specification based on (8), the lagged residual was
highly significant, but no separate partial adjustment process for nominal house
prices was found significant (i.e. b3z = 0). Thus lagged house price changes (∆Pzt–
1) are omitted from the reported results in Table 4. Cross-equation restrictions are
again imposed on the system. The resulting OLS equation is presented as column
(1) in Table 4, where RESt–1 is the lagged residual, using UC2 from the OLS
equation presented in Table 3. Inspection of the estimates in column (1) reveals a
number of features that relate to our tests of short-run efficiency.
First, the coefficient on the lagged residual (b2z) is significantly
negative; its high t-value (18.73) confirms the cointegration findings from Table
3, indicating also that the preferred equation from Table 3 is a valid long-run
equation explaining Pzt. However, the coefficient is significantly different from –
1, with the 95% confidence interval being (–0.48, –0.39). This estimate indicates
that any deviation in house prices from equilibrium in one period is not fully
unwound in the subsequent quarter. Further, the coefficients on ∆Yzt and UC2zt
are well below, and significantly different from, their long-run counterparts; the
coefficient estimate on ∆PCt (which is significantly different from zero) indicates
that around half of consumer price inflation is reflected in house prices
contemporaneously. The only coefficient that is not significantly different to its
long-run counterpart is that on ∆Hzt.
Together, these results indicate that we can reject short-run efficiency in
the sense that prices do not adjust to existing disequilibria or to short-run shocks
within one quarter. Nevertheless, the adjustment parameters are highly significant
and indicate that approximately half the adjustment to most shocks occurs within
a one quarter timeframe.
20
Thus, heuristically, the degree of short-run inefficiency appears small,
especially for a market that does not have freely traded liquid securities.
When including current and lagged sales activity, Szt–i, we tested for
lags individually and also tested whether a group of current and/or lagged
variables was significant. When Szt–2 is included, no other lag of sales is
significant, and Szt–2 always outperformed any other lag of that variable. Thus we
include Szt-2 as our measure of housing market activity. Its coefficient is
particularly interesting in terms of testing for short-run efficiency. Commonly, it
is observed that there is a correlation between sales activity and house prices, but
our results suggest that after controlling for other influences on house prices,
current sales activity has no additional explanatory power. Instead, sales activity
influences house prices with a two-quarter lag. The significant positive value for
this coefficient is contrary to short-run market efficiency. A reasonable
interpretation is that prospective buyers see housing activity lift, decide to embark
on house purchase/sale; there is then a four- to six-month lag between their
observing the housing market activity and their actual market involvement. This
behaviour significantly affects the dynamics of house prices.
The final variable in the equation, COMPzt, is highly significant,
indicating that the composition of houses sold within a quarter affects the median
price observed within a region that quarter. Thus adjusting for this effect is
important given the sales data that we have. The significant positive coefficient on
COMPzt is not an indicator of market inefficiency.
We have run a number of checks on the robustness of the parameters
reported in column (1). Column (2) of Table 4 estimates the same equation using
SUR, using the SUR long-run specification (with UC2) from Table 3. There is
little change to any of the coefficients or to the explanatory power of the equation.
21
Tests of the residuals from the OLS equation in Table 4 indicate the
presence of autocorrelation and heteroskedasticity. In column (3), we present
estimates with panel-corrected standard errors using the Prais-Winsten (PW)
method;25 in column (4) we present generalised least squares (GLS) estimates.26
In each case, there is little difference in coefficient estimates.
4.3 Dynamic results: Asymmetric The potential for asymmetric adjustment was discussed in relation to
(8). Estimates of asymmetric adjustment may be particularly useful in exposing
the circumstances contributing to the short-run inefficiency found above; for
instance, adjustment may be less consistent with market efficiency when the
market is either above or below equilibrium.
In order to investigate the potential for asymmetric adjustment, we re-
estimate column (1) in Table 4, with a dummy term (equal to one when the lagged
residual is positive and zero otherwise) that is interacted with each of the variables
in the equation. This allows us to estimate separate coefficients on each variable
depending on whether the lagged residuals are positive (prices above equilibrium)
or negative. The results of estimating this asymmetric adjustment process, using
OLS, are shown as column (5) in Table 4.27
Several features stand out in these results. First, adjustment to lagged
disequilibrium is estimated to be very much faster than in the symmetric case. The
estimated coefficient is almost identical across negative and positive residuals; we
cannot reject identical coefficients at the 5% significance level. In each case,
however, the coefficient is still significantly different from –1.
25 In the Prais-Winsten regression the disturbances are assumed to be panel-level heteroskedastic in the presence of first-order autocorrelation where the coefficient of the AR(1) process is specific to each panel. 26 The GLS estimates allow for a heteroskedastic error structure with AR(1) autocorrelation specific to each panel. The adjusted R2 and s.e. are not available for this option. 27 SUR estimates provide almost identical results and so are not presented here.
22
Second, house prices adjust symmetrically to contemporaneous
economic activity developments (statistically, we cannot reject symmetry). The
estimated speed of adjustment to economic activity developments is materially
stronger than in the symmetric case, and now represents approximately 80% of the
estimated long-run response. The upper end of the 95% confidence interval in
each case (1.11 and 1.07 with negative and positive residuals respectively) falls
just short of the estimated long-run parameter.
Third, additions to the housing stock have a highly asymmetric effect
on prices. In a depressed housing market, i.e. when house prices are below
equilibrium (negative residual), additions to the housing stock have no effect on
the price; the softening effect of new housing stock on house prices is felt only at
times when the market is buoyant (prices above equilibrium). It is likely that the
house stock expands principally in buoyant rather than depressed times. Thus in
depressed times there is little explanatory power of housing stock changes on
price (hence the parameter estimate which is not significantly different from zero).
The price response to house additions in buoyant times is not significantly
different from the estimated long-run response.
Fourth, the response of house prices to user cost changes is estimated to
be virtually identical in buoyant and depressed conditions. The estimate is
considerably higher than in the equation where symmetry is imposed on all
coefficients and now represents almost 75% of the estimated long-run response.
As in the economic activity case, however, the upper end of the 95% confidence
interval falls just short of the estimated long-run parameter.
Fifth, consumer price inflation is estimated to be fully incorporated into
house prices contemporaneously under buoyant market conditions; under
depressed market conditions only three-quarters of consumer price inflation is
contemporaneously embodied in prices. Symmetry in this respect can be rejected
at the 5% level.
23
Sixth, the effect of lagged sales activity is also highly asymmetric.
When the housing market is depressed, a rise in sales activity boosts prices,
whereas in a buoyant market, a rise in sales activity has no statistically significant
effect on house prices. This result is important for interpreting the role of sales in
creating, or adjusting to, fads. A reasonable interpretation is that buyers and
sellers are aware of market conditions in a buoyant market situation. In a
depressed market people may hold off house purchase (for whatever reasons) but
once people see the housing market starting to move (by observing increased
sales) they enter the market intending to purchase a house prior to prices reverting
to equilibrium. In this case, the sales variable can be considered an equilibrating
factor by speeding the return of prices towards fundamental values within a
depressed market situation. Nevertheless, even though it may be an equilibrating
factor in this respect, its statistical significance is still indicative of the presence of
short-run inefficiency at times in the housing market.
Finally, the explanatory power of the equation is considerably higher
than in the symmetric case. The equation standard error falls by 27% and the
Adjusted R2 more than doubles with the asymmetric estimates relative to the
symmetric case. This material change in explanatory power indicates that
significant asymmetries in the adjustment process exist. When the asymmetric
equation is estimated as two separate equations (split according to the sign of the
residuals), the explanatory power is almost identical across depressed and buoyant
market conditions (with an s.e. of 0.0267 and 0.0265 respectively). Thus house
price changes are equally explicable in depressed and buoyant conditions, but
material differences are found in the role of some variables, especially housing
stock changes, consumer price inflation and sales activity. A comparison of
column (1) and column (5) in Table 4 indicates that the linear model needs to
incorporate asymmetric adjustment. (5) is therefore our preferred short-run, linear
equation.
24
4.4 Dynamic results: Non-linear The short-run estimates have hitherto constrained the dynamics to be
linear (albeit asymmetric). They have so far ignored the potential for non-linear
adjustment embodied in coefficients b2Az and b3Az in (8). The significance of the
sales variable in the previous dynamic specifications suggests it is particularly
important to investigate potential non-linearities associated with improved
information dissemination arising from increased sales activity. We do so initially
based on the symmetric specification reported as column (1) in Table 4, and then
with asymmetries. In each case, we ignore the role of b3Az since we detect no
significant role for lagged price changes in the adjustment process.
In implementing (8) we must decide whether to set Ā as the national
mean of the housing market activity variable or as the regional mean, the latter
varying across regions. It is possible, for instance, that information dissemination
may be region-specific, in which case the latter variable will be more relevant, but
if information dissemination is nationwide the national mean is relevant.
We estimate both regional and national versions of (8). In each case, we
use the sales variable, Szt, for our measure of housing market activity. The results
from using the national and regional means are almost identical and there is little
to choose statistically between specifications. Coefficients on each of the variables
within the equation (including the lagged sales variable) are hardly altered by the
alternative measures. The interaction term (b2Az) is statistically significant in each
specification ("t-values" for the national specification are 3.36 and 3.58 for OLS
and SUR respectively; and for the regional specification they are 2.92 and 2.68
respectively).
The b2Az coefficient in each case is positive, implying that a higher sales
ratio leads to slower adjustment to disequilibrium. The effect, however, is small.
A 10% increase in Szt is estimated to alter the adjustment term on the residual
from –0.414 to –0.379, implying little material shift in adjustment to
disequilibrium. (This estimate is based on the OLS national specification; other
specifications are similar.)
25
The direction of this result contrasts with the information-based reason
put forward by Capozza et al for including the interaction term, since higher sales
activity should improve information dissemination, therefore leading to faster
adjustment to disequilibrium. An alternative explanation, consistent with the
results here, is that high current sales activity has some fad element associated
with it. For instance, in a buoyant market, high sales activity may delay
adjustment back to fundamentals when price is above equilibrium.
We shed light on this potential explanation by re-estimating (8), using
the national mean, with asymmetric adjustment depending on whether lagged
residuals are positive or negative. We find that the interaction term is not
statistically significant when the market is depressed but is just significant (at the
10% level in each of the OLS and SUR approaches) in a buoyant market. This
result suggests that high sales activity has a slight delaying effect on adjustment to
fundamentals in a buoyant market. Again, however, the effect is not material in an
economic sense (a 10% increase in Szt in a buoyant market reduces the adjustment
term on the residual from –0.697 to –0.673). Given the lack of materiality of the
non-linear adjustment process—both symmetric and asymmetric—our
interpretation of results henceforth concentrates on the linear asymmetric results,
i.e. column (5) of Table 4.
5 Interpretation To interpret our results and to apply them to recent housing market
experience internationally, we examine the potential for overshooting or other fad-
like (bubble) phenomena to arise consistent with our estimates. Taking the long-
run (Table 3) and dynamic asymmetric OLS estimates (column 5 in Table 4) as
our starting points, we trace out the dynamic effect of a realistic change to real
economic activity on the real median house price. Initially we hold all other
factors constant (i.e. we do not consider any flow-on effects to sales activity, etc)
other than expectations which follow the extrapolative form estimated (within
UC2) in the long-run equation. Subsequently, we examine the effect of
interactions with house sales.
26
The economic activity change that we consider is based on actual
aggregate US GDP experience since 1985.28 In the decade to 1995q2, real GDP
grew at an average rate of 0.72% per quarter (p.q.). Over the following five years
(to 2000q2) the average growth rate was 1.05% p.q.; in the following two years
(to 2002q2) average growth fell to 0.25% p.a. We take, as our baseline, a GDP
(economic activity) growth rate of 0.72% p.q. and calculate the real house price
corresponding to this track, holding other variables constant. We then compare the
house price arising from a "shocked" GDP track and express this latter track as a
percentage of baseline. The shocked track that we compare is one that historically
grows at 0.72% p.q.; then (from quarter 1) experiences growth of 1.05% p.q. for
20 quarters, then 0.25% p.q. growth for the following 8 quarters, thereafter
returning to 0.72% quarterly growth.29
Figure 1 graphs the resulting real house price path expressed as a
percentage of baseline. The GDP track results in the long-run level of GDP in the
shocked case settling 2.9% higher than baseline. This has the effect of raising
long-run real house prices by 3.4% relative to baseline. In the interim, however,
house prices rise to a peak at 8.2% above baseline (after 20 quarters) before
dropping to 3.1% above baseline (after 35 quarters), thence returning to the long-
run value.
In part, this behaviour is driven by the faster then slower path for GDP
growth. But it is also affected by the expectations adjustment mechanism that
feeds into the user cost variable. This mechanism can be seen from Figure 2. This
figure graphs the real house price path consequent on a permanent 1% innovation
to economic activity. The long-run house price effect of the activity increase is
1.17%; the contemporaneous effect is 0.89%. The initial house price increase
feeds into real capital gains expectations via the UC variable so that UC falls
consequent to the house price rise.
28 US GDP data underlying these calculations is sourced from Bureau of Economic Analysis, US Department of Commerce. 29 While this period involves quite a stark cycle for the US, we note that individual regional economies, as discussed by Case and Shiller (2003), have undergone considerably larger economic activity cycles with the potential for considerably magnified housing cycles relative to the aggregate experience.
27
The fall in UC is magnified as the house price rise continues, and this
fall contributes to a further rise in the house price. The combined effect of this
process and the direct effect of regional activity on house prices is to cause an
overshooting of house prices above the long-run equilibrium. At some point, the
positive residual created through house prices being above equilibrium exerts
downward price pressure, equilibrating the market. A damped cycle results, as
depicted in Figure 2. The peak of the cycle occurs in the 13th quarter, with a price
rise (above baseline) of 1.24%. The trough occurs in the 26th quarter, just below
the long-run value.
Endogenous sales activity is a factor which may make for additional
complexity in the dynamics. Sales activity may respond to the price dynamics, i.e.
to the change in prices and/or to the disequilibrium in prices. If that is the case, the
presence of a significant sales effect in the dynamic price equation will affect the
price path in response to a shock. To illustrate the effect of sales, we estimate a
simple equation for Szt as a function of current and lagged changes in real house
prices (∆Pzt–i) and the lagged residual from the long-run house price equation
(RESzt–1). Coefficients on these terms are restricted across regions, but constant
and quadratic time trend terms are included and vary across regions to allow for
region-specific fixed and trend effects. Estimates are presented in Table 5.
The estimates in Table 5 indicate that sales activity increases with
current and lagged (real) price rises. The effect is strongest as a result of one
quarter lagged price changes, with a decreasing effect thereafter, up to five
quarters. This effect may contribute to a disequilibrating dynamic given that
lagged sales in turn positively affect price changes. However, sales activity is also
estimated to decrease as prices rise beyond their long-run value via the negative
coefficient on the residual term. This has an equilibrating effect on the market
given the lagged sales effect on prices.
Combining the dynamic equation for sales with the long-run and
dynamic (asymmetric) price estimates, we calculate the price effect of an activity
rise allowing for the interaction of direct price effects, the UC effect and the sales
effect.
28
In the case of a 1% permanent increase in economic activity, there is a
slightly greater degree of price overshooting than observed previously (with
exogenous sales activity). The speed of the overshooting occurs considerably
faster, with the peak being reached in the fourth quarter. (Apart from the speed of
the overshooting, the other properties of the cycle remain similar to those shown
in Figure 2 and so are not reproduced here.)
In response to a permanent 1% reduction in activity, a much slower
cycle is exhibited with endogenous sales, with the trough in prices occurring in
the ninth quarter. The reason for this asymmetry is the asymmetric adjustment of
prices to sales. With a positive shock, the contemporaneous price rise is initially
less than the long-run rise, resulting in a negative residual. The negative residual
in turn causes a sales rise in excess of that driven by the initial price change, and
the compound rise in sales further boosts prices (with a two-quarter lag)
contributing to the speed of the overshooting. By contrast, a negative shock results
in a positive residual (as prices initially fall less than the long-run fall) but in this
case there is no material price response to sales because of the asymmetric effect
of sales on price dynamics. Thus the effect of the shock takes longer to feed
through to prices and overshooting occurs more gradually. This asymmetry
mirrors the findings of Genesove and Mayer's (2001) "reluctant-seller" case
whereby a negative localised shock leads to slower house price adjustment to
equilibrium than is the case with a positive shock.
Overall, our estimates indicate that realistic changes in the path of
economic activity can have a material effect on house prices, causing prices to
overshoot their long-run equilibrium. Both extrapolative expectations effects and
sales dynamics are shown to impact on the cycles that emerge from changes to
underlying economic factors, while asymmetries in adjustment may be material.
29
6 Conclusions Consistent with our theoretical model based on consumer optimisation
conditions, regional real house prices converge to a long-run equilibrium
determined by regional economic activity, the regional housing stock and the user
cost of capital. Trend variables, reflecting trends in housing services and amenity
values, have a significant impact in eleven of the fourteen regions.
In contrast with the long-run results, the strict conditions for short-run
efficiency are not met. House prices respond to contemporaneous shocks in the
directions expected and respond significantly to lagged disequilibrium in prices.
However, adjustment is not fully completed within one quarter either to
contemporaneous shocks or to lagged disequilibrium. Adjustment is symmetric in
response to lagged disequilibrium and to contemporaneous shocks to economic
activity and to the user cost of capital, but is asymmetric in response to consumer
price changes. Further, house prices respond positively to past house sales
activity, but only in depressed market conditions (when prices are below
equilibrium).
The presence of a significant positive sales effect would normally be
considered to contribute to price overshooting following a shock to fundamentals
(for example, to economic activity). This is especially the case when sales activity
is itself a positive function of past house price changes, as indeed we find. In the
case of our estimates, however, the sales effect is an equilibrating influence, only
driving prices upwards (towards equilibrium) when prices are below their
equilibrium levels. When prices exceed equilibrium, the sales effect is absent.
Our estimates indicate that extrapolative house price expectations,
based on medium-term regional price trends, provide the best explanation
(amongst the expectations proxies we examined) of house price developments
when incorporated into the user cost of capital measure. Our simulations of house
price responses to economic activity shocks demonstrate that this expectations
process induces some mild overshooting of house prices following an economic
activity shock. These results are consistent with the survey-based findings of Case
and Shiller (2003).
30
The length of the cycle depends on whether the activity shock is
positive or negative (the latter having the longer cycle), reflecting the asymmetric
influence of house sales activity on real house prices. The latter effect is
consistent with sellers being reluctant to sell their houses when equilibrium prices
have fallen following a negative economic shock.
Although our results reject short-run efficiency, heuristically the degree
of housing market inefficiency appears small. Approximately three-quarters of
lagged disequilibrium disappears within three months. A similar fraction of the
long-run price effects from economic activity and user cost of capital shocks are
reflected contemporaneously in house prices. Three-quarters of consumer price
changes are reflected contemporaneously in house prices in depressed market
conditions and the full effect of consumer price changes is contemporaneously
impounded in house prices in buoyant conditions. Nevertheless, our estimates
indicate that adjustment to equilibrium is characterised by asymmetries and some
degree of overshooting. Thus the housing market, while being "moderately
efficient", retains the capability for delivering surprising and potentially
destabilising episodes.
31
Table 1: Sales price summary statistics, population and activity Regional council
2002 median sales price ($000)*
Real % price change: 1981–2002
Average no. quarterly sales
Population (2001 census)
Population density (2001 census)
% change in real economic activity: 1981–2002
RC01 157 46 568 140,133 10.1 105
RC02 282 111 5349 1,158,891 206.9 98
RC03 166 61 1658 357,726 14.0 92
RC04 168 38 1270 239,412 19.2 84
RC05 100 2 168 43,974 5.3 32
RC06 142 32 616 142,947 10.1 64
RC07 106 12 524 102,858 14.1 73
RC08 98 12 1191 220,089 9.9 51
RC09 203 87 2206 423,765 52.2 77
RC11 162 46 669 122,475 5.4 97
RC12 63 24 173 30,303 1.3 62
RC13 146 58 2727 481,431 10.6 99
RC14 117 38 1158 181,542 5.7 59
RC15 66 –27 578 91,002 2.6 46
*Expressed in $NZ. On average, over 2002, NZ$1 = US$0.46.
Table 2: Results of panel unit root tests Levin-Lin-Chu Im-Pesaran-Shin
Variable Trend and constant
Constant Trend and constant
Constant
Pz I(0)/I(1) I(0)/I(1) I(0)/I(1) I(0)/I(1)
Yz I(1) I(1) I(1) I(1)
Sz I(0)/I(1) I(0)/I(1) I(0) I(0)
Hz I(0) I(0) I(0) I(1)
UC2z I(1) I(0) I(1) I(0)
UC3z I(1) I(1) I(1) I(1)
COMPz I(0) I(0) I(0) I(0)
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Table 3: Long-run house price estimates UC1 UC2 UC3 UC4
OLS SUR OLS SUR OLS SUR OLS SUR
Yzt 1.372
(24.87)
1.198
(24.43)
1.169
(22.82)
0.921
(18.49)
1.575
(30.42)
1.331
(27.02)
1.577
(29.89)
1.338
(26.75)
H zt -0.582
(7.30)
-0.598
(10.93)
-0.691
(9.43)
-0.646
(11.89)
-0.671
(7.90)
-0.723
(12.46)
-0.470
(5.95)
-0.456
(8.37)
UC zt -0.0057
(10.46)
-0.0062
(9.26)
-0.0077
(20.06)
-0.0097
(24.66)
-0.0044
(7.92)
-0.0053
(8.14)
-0.0031
(3.16)
-0.0038
(2.85)
UCDt 0.0759
(7.52)
0.0625
(4.85)
0.0500
(5.96)
0.0223
(1.87)
0.1154
(13.55)
0.1013
(8.40)
0.1093
(8.58)
0.0879
(5.04)
Adj.
R2
0.9979 0.9729 0.9980 0.9780 0.9974 0.9724 0.9979 0.9706
s.e. 0.0542 0.0545 0.0485 0.0491 0.0544 0.0550 0.0560 0.0567
Obs 1,232 1,232 1,232 1,232 1,232 1,232 1,232 1,232
All equations are estimated over 1981(1)–2002(4). Absolute t statistics in parentheses. Each equation has unrestricted constants, TIME and TIME2, included but not reported. The dependent variable is the log of real house prices (Pzt), where z denotes region,and t denotes time. Yzt is the log of real regional economic activity. Hzt is the log of housing stock. UCzt is the user cost of capital [definitions as in the text, entered only from 1985(1) onwards]. UCDt is a dummy variable equal to 1 to 1984(4) and equal to 0 thereafter to account for the regulated financial system.
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Table 4: Dynamic house price estimates (1)
OLS
symmetric
(2)
SUR
symmetric
(3)
PW
symmetric
(4)
GLS
symmetric
(5)
OLS
asymmetric
-ve RESt-1 +ve RESt-1
RESzt–1 -0.4326*** -0.4255*** -0.4681*** -0.4507*** -0.7473*** -0.7196***
(18.73) (18.66) (16.22) (19.64) (27.34) (26.41)
∆Yzt 0.6320*** 0.5682*** 0.5925*** 0.5211*** 0.9293*** 0.8949***
(7.16) (6.43) (6.45) (6.73) (9.94) (9.77)
∆Hzt -0.7900*** -0.6266** -0.7202** -0.6298** 0.2383 -0.8109***
(2.70) (2.14) (2.43) (2.38) (0.79) (2.66)
∆UC2zt -0.0017** -0.0017** -0.0016** -0.0017*** -0.0057*** -0.0056***
(2.36) (2.45) (2.20) (2.86) (6.83) (8.04)
COMPzt 0.1490*** 0.1436*** 0.1673*** 0.1464*** 0.1184*** 0.0827***
(8.40) (8.11) (8.02) (8.59) (5.87) (4.85)
Szt–2 1.2656*** 1.2765*** 1.1701*** 1.0693*** 1.3476*** 0.0652
(5.78) (5.83) (4.84) (5.31) (5.85) (0.29)
∆PCt -0.4941*** -0.4787*** -0.5366*** -0.5409*** -0.2645*** 0.0138
(6.02) (5.82) (6.29) (7.53) (3.28) (0.14)
Obs. 1204 1204 1204 1204 1204
Adj. R2 0.3057 0.3046 0.3251 0.6337
s.e. 0.0366 0.0366 0.0361 0.0266
The dependent variable is the log change in real house prices (∆Pzt), where z denotes region, t denotes time. RESzt–1 is the lagged long-run house price residual from Table 3. ∆Yzt is the log change in real regional economic activity. ∆Hzt is the log change in housing stock. UC2zt is change in user cost of capital (the second proxy for ġ in the text). COMPzt is a housing stock composition variable. Szt–2 is house sales to housing stock ratio lagged two quarters. ∆PCt is the log change in consumer prices. An unrestricted constant term is included but not reported. Absolute t statistics in parentheses; * indicates significant at 10%; ** significant at 5%; *** significant at 1%.
34
Table 5: Sales (Szt) response to house price developments OLS
RESzt–1 –0.0196
(–7.70)***
∆Pzt 0.0080
(3.34)***
∆Pzt–1 0.0258
(10.01)***
∆Pzt–2 0.0186
(7.89)***
∆Pzt–3 0.0081
(3.60)***
∆Pzt–4 0.0073
(3.30)***
∆Pzt–5 0.0059
(2.76)***
Adjusted R2 0.69
The dependent variable is house sales to housing stock ratio (Szt) where z denotes region, t denotes time. RESz–-1 is the lagged long-run house price residual from Table 3 column (1). ∆Pzt is the log change in real house price. Unrestricted constants TIME and TIME2 included but not reported. Absolute t statistics in parentheses; *** indicates significant at 1%.
35
Figure 1: Real house price response to simulated changes in economic activity
100
101
102
103
104
105
106
107
108
109
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61
Quarter
Hou
se P
rice
(% o
f Bas
elin
e)
Figure 2: Real house price response to 1% increase in economic activity
99.8
100
100.2
100.4
100.6
100.8
101
101.2
101.4
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61
Quarter
Hou
se P
rice
(% o
f Bas
elin
e)
36
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Banerjee, A., J.D. Dolado, J.W. Galbraith and D.F. Hendry. 1993. Co-integration, error correction, and the econometric analysis of non-stationary data, Oxford: Oxford University Press.
Can, A. 1992. “Specification and estimation of hedonic housing price models,” Regional Science and Urban Economics, 22:3, pp. 453–474.
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Case, Karl and Christopher Mayer. 1996. “Housing price dynamics within a metropolitan area,” Regional Science and Urban Economics, 26:3-4, pp. 387–407.
Case, Karl and Robert Shiller. 1988. “The behaviour of home buyers in boom and post-boom markets,” New England Economic Review, Nov/Dec, pp. 29–46.
Case, Karl and Robert Shiller. 1989. “The efficiency of the market for single family homes,” American Economic Review, 79:1, pp. 125–137.
Case, Karl and Robert Shiller. 2003. “Is there a bubble in the housing market? An analysis,” Paper prepared for the Brookings Panel on Economic Activity, September.
Cook, Stephen. 2003. “The convergence of regional house prices in the UK,” Urban Studies, 40:11, pp. 2285–2294.
Di, Zhu Xio. 2001. “The role of housing as a component of household wealth,” Working Paper W01-6, Joint Center for Housing Studies, Harvard University, Cambridge, MA.
Dubin R.A. 1992. “Spatial autocorrelation and neighborhood quality,” Regional Science and Urban Economics, 22:3, pp. 433–452.
Genesove, David and Christopher Mayer. 2001. “Loss aversion and seller behaviour: Evidence from the housing market,” Quarterly Journal of Economics, 116:4, pp. 1233–1260.
Glaeser, Edward and Joseph Gyourko. 2001. “Urban decline and durable housing,” Discussion Paper 1931, Harvard Institute of Economic Research, Harvard University, Cambridge, MA.
Glaeser, Edward and Joseph Gyourko. 2002. “The impact of zoning on housing affordability,” Discussion Paper 1948, Harvard Institute of Economic Research, Harvard University, Cambridge, MA.
Grimes, Arthur. 1994. “The determinants of mortgage rates,” National Bank of New Zealand Economics Working Paper 94-1, National Bank of New Zealand, Wellington.
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Im, K.S., M.H. Pesaran and Y. Shin. 2003. “Testing for unit roots in heterogeneous panels,” Journal of Econometrics, 115:1, pp. 53–74.
Levin, A., C-F. Lin and C-S.J. Chu. 2002. “Unit root tests in panel data: Asymptotic and finite-sample properties,” Journal of Econometrics, 108:1, pp. 1–24.
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Motu Economic and Public Policy Research Motu Economic and Public Policy is a non-profit Research Institute (Charitable Trust) that has been registered since 1 September 2000. The Trust aims to promote well-informed and reasoned debate on public policy issues relevant to New Zealand decision making. Motu is independent and does not advocate an expressed ideology or political position.
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Motu Working Paper Series 04–01. Kerr, Suzi; Andrew Aitken and Arthur Grimes, “Land Taxes and Revenue Needs as Communities Grow and Decline: Evidence from New Zealand”. 03–19. Maré, David C, “Ideas for Growth?” 03–18. Fabling, Richard and Arthur Grimes, “Insolvency and Economic Development:Regional Variation and Adjustment”. 03–17. Kerr, Suzi; Susana Cardenas and Joanna Hendy, “Migration and the Environment in the Galapagos:An analysis of economic and policy incentives driving migration, potential impacts from migration control, and potential policies to reduce migration pressure”. 03–16. Hyslop, Dean R. and David C. Maré, “Understanding New Zealand’s Changing Income Distribution 1983–98: A Semiparametric Analysis”. 03–15. Kerr, Suzi, “Indigenous Forests and Forest Sink Policy in New Zealand”. 03–14. Hall, Viv and Angela Huang, “Would Adopting the US Dollar Have Led To Improved Inflation, Output and Trade Balances for New Zealand in the 1990s?” 03–13. Ballantyne, Suzie; Simon Chapple, David C. Maré and Jason Timmins, “Movement into and out of Child Poverty in New Zealand: Results from the Linked Income Supplement”. 03–12. Kerr, Suzi, “Efficient Contracts for Carbon Credits from Reforestation Projects”. 03–11. Lattimore, Ralph, “Long-run Trends in New Zealand Industry Assistance”. 03–10. Grimes, Arthur, “Economic Growth and the Size & Structure of Government: Implications for New Zealand”. 03–09. Grimes, Arthur; Suzi Kerr and Andrew Aitken, “Housing and Economic Adjustment”. 03–07. Maré, David C. and Jason Timmins, “Moving to Jobs”. 03–06. Kerr, Suzi; Shuguang Liu, Alexander S. P. Pfaff and R. Flint Hughes, “Carbon Dynamics and Land-Use Choices: Building a Regional-Scale Multidisciplinary Model”. 03–05. Kerr, Suzi, “Motu, Excellence in Economic Research and the Challenges of 'Human Dimensions' Research”. 03–04. Kerr, Suzi and Catherine Leining, “Joint Implementation in Climate Change Policy”. 03–03. Gibson, John, “Do Lower Expected Wage Benefits Explain Ethnic Gaps in Job-Related Training? Evidence from New Zealand”. 03–02. Kerr, Suzi; Richard G. Newell and James N. Sanchirico, “Evaluating the New Zealand Individual Transferable Quota Market for Fisheries Management”. 03–01. Kerr, Suzi, “Allocating Risks in a Domestic Greenhouse Gas Trading System”. All papers are available online at http://www.motu.org.nz/motu_wp_series.htm
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